The domain of the function $f (x) = {log}_{x} (cos x)$ is

(- \frac{π}{2}, \frac{π}{2}) - {1}

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(\frac{π}{2}, \frac{π}{2}) - {1}

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(- \frac{π}{2}, \frac{π}{2})

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(0, \frac{π}{2}) - {1}

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Solution

The correct option is A $(- \frac{π}{2}, \frac{π}{2}) - {1}$
$f (x) = {l o g}_{x} c o s x = \frac{l o g (c o s x)}{l o g x}$
Since $c o s x$ is +ve in $(- \frac{π}{2}, \frac{π}{2})$
$∴ l o g (c o s x)$ is defined in $(- \frac{π}{2}, \frac{π}{2})$
$\frac{1}{l o g x}$ is undefined at $x = 1$
$∴$ Domain of $f (x) = {l o g}_{x} (c o s x)$ is $(- \frac{π}{2}, \frac{π}{2}) - {1}$

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